Photonic crystal masers

ABSTRACT

In a general aspect, a photonic crystal maser includes a dielectric body having an array of cavities ordered periodically to define a photonic crystal structure in the dielectric body. The dielectric body also includes a region in the array of cavities defining a defect in the photonic crystal structure. An elongated slot through the region extends from a slot opening in a surface of the dielectric body at least partially through the dielectric body. The array of cavities and the elongated slot define a waveguide having a waveguide mode. The photonic crystal maser also includes a vapor or source of the vapor in the elongated slot and a laser configured to generate an optical signal capable of exciting one or more input electronic transitions of the vapor.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.63/107,924, which was filed on Oct. 30, 2020 and entitled, “PhotonicCrystal Maser.” The disclosure of this priority application is herebyincorporated by reference in its entirety.

BACKGROUND

The following description relates to photonic crystal masers.

Masers produce coherent electromagnetic radiation through stimulatedemission by atoms or molecules from a higher energy state to a lowerenergy state. The stimulated emission produces electromagnetic radiationat an emission frequency of the atoms or molecules that builds up in aresonator. A resonator may be used to capture a portion of thestimulated emission from the atoms or molecules so that the photons inthe resonator can stimulate more emission into the resonator mode fromexcited atoms or molecules. To do so, the resonator may have a mode ofoscillation that corresponds to the emission frequency of the atoms andmolecules, thereby allowing the resonator to “resonate” with the atomsor molecules. The resonator may thus store energy—and by coherent,stimulated emission—amplify the emission of electromagnetic energy fromthe maser.

DESCRIPTION OF DRAWINGS

FIG. 1A is a schematic diagram, in perspective view, of an examplephotonic crystal maser that includes a dielectric body bonded to twooptical windows;

FIG. 1B is a schematic diagram, in top view, of the example photoniccrystal receiver of FIG. 1A, but in which the dielectric body includes aring resonator structure;

FIG. 2 is a schematic diagram of example energy levels for a Rydbergatom maser;

FIG. 3A is a contour map of an electric field, generated in response toa simulated dipole oriented normal to the top surface, for an examplephotonic crystal maser having a resonant frequency of 81.8 GHz;

FIG. 3B is a contour map of the electric field of FIG. 3A, but in whichthe scale is increased by 1000;

FIG. 3C is a contour map of the electric field of FIG. 3A, but in whichthe simulated dipole oscillates at 81.7 GHz and is oriented parallel toa top surface of the example photonic crystal maser;

FIG. 3D is a contour map of the electric field of FIG. 3A, but in whichthe simulated dipole oscillates at 81.8 GHz and is oriented parallel toa top surface of the example photonic crystal maser;

FIG. 3E is a contour map of the electric field of FIG. 3A, but in whichthe simulated dipole oscillates at 82.0 GHz and is oriented parallel toa top surface of the example photonic crystal maser;

FIG. 4A is a schematic diagram of a cross-section of an example photoniccrystal maser that has an optical window and a movable glass piecepositioned above the optical window;

FIG. 4B is a graph of a band edge of the example photonic crystal maserof FIG. 4A, showing how a position of the movable glass piece shifts afrequency position of the band edge;

FIG. 5 is a contour map of an electric field magnitude through across-section of an example photonic crystal structure;

FIG. 6A is a schematic diagram, in perspective and top views, of anexample photonic crystal maser that is being optically pumped by alaser;

FIG. 6B is a schematic diagram, shown in perspective, of the examplephotonic crystal maser of FIG. 6A, but in which miniature couplingoptics are used to direct light from a pump laser into the examplephotonic crystal maser;

FIG. 6C is a schematic diagram, in top view, of the example photoniccrystal maser of FIG. 6A, but in which miniature coupling optics areused to direct light from a pump laser into the example photonic crystalmaser;

FIG. 7A is a schematic diagram, in perspective view, of an examplephotonic crystal maser used to determine the enhancement factor for aradiating dipole;

FIG. 7B is a graph of the enhancement factor simulated for the examplephotonic crystal structure of FIG. 7A;

FIG. 8 is a table of example design parameters for a photonic crystalmaser;

FIG. 9A is a schematic view, in top view, of an example photonic crystalstructure having cavities configured to define a photonic crystal mirrorproximate an end of an elongated slot;

FIG. 9B is a contour graph of electric field pattern for the examplephotonic crystal structure of FIG. 9A that corresponds to a 97.8%reflection from the photonic crystal mirror;

FIG. 9C is a contour graph of electric field pattern for the examplephotonic crystal structure of FIG. 9A that corresponds to an 88.5%reflection from the photonic crystal mirror;

FIG. 9D is a table of reflectivity values for the photonic crystalmirror of FIG. 9A resulting from various scaling factors;

FIG. 10 is a schematic diagram of an example testing system thatincludes a photonic crystal maser;

FIG. 11 is a schematic diagram of an example transceiver system thatincludes two transceivers, each having a photonic crystal maser and aphotonic crystal receiver; and

FIG. 12 a schematic diagram of a system that includes a photonic crystalmaser and a vapor cell sensor.

DETAILED DESCRIPTION

In a general aspect, a photonic crystal maser is disclosed that includesa photonic crystal structure and a vapor therein. For example, thephotonic crystal maser may include a dielectric body having an array ofcavities ordered periodically to define a photonic crystal structure inthe dielectric body. The dielectric body may also include a region inthe array of cavities defining a defect in the photonic crystalstructure. An elongated slot through the region extends from a slotopening in a surface of the dielectric body at least partially throughthe dielectric body. The photonic crystal maser may also include a vapor(or a source of the vapor) in the elongated slot and an optical windowcovering the elongated slot. The optical window has a window surfacebonded to the surface of the dielectric body to form a seal about theslot opening. In doing so, the optical window may define the vapor cellwith the dielectric body. In some variations, the photonic crystalstructure and the elongated slot are configured to be resonant with anelectronic transition of the vapor (e.g., a Rydberg transition, anatomic transition, a molecular transition, etc.). In some variations, anoptical mirror is placed at one or both ends of the elongated slot. Insome variations, a photonic crystal mirror is placed at one or both endsof the elongated slot. Other configurations of the photonic crystalmaser are possible, as described below.

In some implementations, a photonic crystal maser may be constructed bycreating a photonic crystal frame (or structure) and then bonding one ortwo optical windows to the frame. These components may be bonded to eachother using techniques described in U.S. Pat. No. 10,859,981 entitled“Vapor Cells Having One or More Optical Windows Bonded to a DielectricBody,” and U.S. Pat. No. 11,137,432 entitled “Photonic CrystalReceivers,” the disclosures of which, are incorporated herein byreference in their entirety. For example, a contact bonding method maybe used to bond the photonic crystal frame to one or both opticalwindows. Moreover, an adhesion layer may be used to facilitate bondingthe photonic crystal frame to one or both optical windows (e.g., anadhesion layer formed of silicon or silicon dioxide).

The photonic crystal frame and optical windows may be formed ofdielectric material. For example, the photonic crystal frame may beformed from silicon and the optical windows may be formed from glass(e.g., a borosilicate glass, a fused silica glass, etc.). As anotherexample, the photonic crystal frame, the optical windows, or both may beformed of BaLn₂Ti₄O₁₂ (BLT) where Ln corresponds to one or more elementsselected from the lanthanide elements. In many variations, the opticalwindows are transparent to laser light used to pump the maser. Thistransparency may occur throughout an optical window, or alternatively,be limited to a portion of the optical window, such as a portioncovering the elongated slot.

In some implementations, the vapor includes gaseous atoms, molecules, orboth. The vapor, or generally emitters, is located in the elongated slotcentered in a defect of the photonic crystal (e.g., a linear defect).This location allows the vapor to experience a different electromagneticmode environment than in free space. In many variations, the modestructure of the electromagnetic field is modified by the presence ofthe photonic crystal frame. The photonic crystal frame may also bedesigned to slow an electromagnetic wave by increasing the groupvelocity index of refraction at and around a specific design frequency.Slowing the electromagnetic wave may increase the stimulated emissionrate of the emitters into that mode by increasing the energy density inthe cavity relative to free-space. The slowed electromagnetic wave maybe largely confined to the elongated slot, which may further intensifythe electromagnetic field (e.g., by modifying the resonant mode).

One advantage of this configuration is that the slowing andconcentration of the electromagnetic field can lower the masingthreshold by increasing the emission rate into the resonant mode. Suchlowering allows maser action at lower gain since the gain threshold islowered. The local field modes at the resonant frequency may be designedto correspond to a specific transition frequency of the vapor residingin the elongated slot. In some instances, color centers or othermaterials may be placed in the elongated slot. The rate of emission intothese modes can be significantly increased relative to emission intoother electromagnetic field modes, for example, modes corresponding todirections orthogonal to the elongated slot or other frequencies.

In some instances, a maser is initiated by creating an inversion on ahigh lying transition of the emitters placed inside the elongated slot,such as by laser excitation of a high lying Rydberg state. For example,a pump laser(s) can be coupled into the elongated slot using mirrors andfiber optics. Spontaneous emission into the slot-photonic crystal modetriggers an avalanche of stimulated emission into this mode, creating amaser. The masing process may produce a coherent, directed source ofelectromagnetic waves at the design frequency. The ends of the elongatedslot and photonic crystal frame can be constructed as mirrors for themaser by changing the geometry of the photonic crystal. Moreover,multiple passes of the wave through the elongated slot can be designedinto the structure allowing for greater amplification of theelectromagnetic wave. In some variations, a taper located adjacent tothe output mirror can be used to couple the output electromagnetic waveto free space and shape the output beam. Other structures for shapingthe beam at the output are possible, such as a lens. The device may beamplitude modulated by modulating the pumping (e.g., modulating anintensity of the laser light).

In some implementations, low temperature contact bonding is used forvacuum sealing, such as described in U.S. Pat. Nos. 10,859,981 and11,137,432. One of the optical windows—or a fill hole in one of theoptical windows—can be contact bonded so that the atomic sample remainspure. Other methods of bonding may require high temperatures and/orvoltages be applied to the vapor cell leading to significant outgassing,which can compromise the performance of the maser due to collisions. Incertain cases, a small stem may be used for filling the vapor cell. Inthese cases, the optical windows can be anodically bonded to the frame.The structure is made of all-dielectric materials. Such constructionallows the maser to be used for over-the-air testing in anechoicchambers as a signal source or used in directional communicationssystems. The maser may also be used as a clock, or frequency reference,and as a local oscillator for signal processing in receiverapplications. Furthermore, the maser may be integrated with theprinciples of Rydberg atom electrometry to construct a jointemitter-receiver in accordance with the disclosure herein.

In some implementations, the photonic crystal masers may producecoherent radiation in the radio frequency (RF) regime (e.g., 100 MHz-1THz), and as such, may function similar to a laser emittingradio-frequency (RF) electromagnetic radiation. In some variations, theregime ranges from 20 kHz to 1 THz. In further variations, the regimeranges from 20 kHz to 300 GHz. The photonic crystal maser may include amonolithic photonic crystal frame, with a vapor cell incorporatedtherein, to construct a maser that can produce powers up to about 100nW. Although the power is low, the device may be fabricated fromdielectric materials and can be used to produce directed RF signals forover-the-air testing and communications. The emitted beam can bedirectional and coherent, allowing propagation for long distanceswithout the spatial spread commonly produced by antennas. Such spatialspread leads to a R⁻² reduction in the beam intensity, where R is thepropagation distance. The dielectric construction of the photoniccrystal maser allows it to sit in an anechoic chamber and producemodulated RF signals for testing without significantly perturbing theenvironment. Photonic crystal masers can also be used for timing andfrequency referencing, RF spectroscopy, or as a local oscillator inconjunction with a Rydberg atom-based receiver or other type ofconventional receiver.

In some examples, a photonic crystal maser includes the photonic crystalstructure (or frame) and a fiber optic circuit to channel pump laserlight into an elongated slot of the photonic crystal structure. Thephotonic crystal maser may also include one or more pump lasers andelectronics to control these lasers. The electronics may also control anoutput coupler, or other structure, to shape (e.g., collimate) theoutput beam from the pump laser and impedance match the output beam to apropagation medium.

For example, FIG. 1A presents a schematic diagram, in perspective view,of an example photonic crystal maser 100 that includes a dielectric body102 bonded to two optical windows 104, 106. The dielectric body 102includes an array of cavities 108 ordered periodically to define aphotonic crystal structure 110 in the dielectric body 102. For example,the cavities 108 of the array may be disposed on respective sites of atwo-dimensional lattice, such as an oblique lattice, a square lattice, arectangular lattice, a hexagonal lattice, a rhombic lattice, and soforth. In FIG. 1A, each cavity 108 is defined by a through-hole.However, other shapes are possible for the cavities 108 (e.g., blindholes, internal voids, etc.), including combinations of shapes. Thedielectric body 102 also includes a region 112 (or defect region) in thearray of cavities 108 defining a defect in the photonic crystalstructure 110. The region may be defined by an absence of cavities 108on two or more contiguous sites of a two-dimensional lattice. In FIG.1A, the region 112 is a linear region having a row of cavities 108absent. However, other geometries are possible, including curved,circular, elliptical, serpentine, square, rectangular, hexagonal, and soforth.

The dielectric body 102 may be formed of a material substantiallytransparent to RF electromagnetic radiation. The material may be aninsulating material having a high resistivity, e.g., ρ>10³ Ω·cm, and mayalso correspond to a single crystal material, a polycrystallinematerial, or an amorphous (or glass) material. For example, thedielectric body 102 may be formed of silicon. In another example, thedielectric body 102 may be formed of a glass that includes silicon oxide(e.g., SiO₂, SiO_(x), etc.), such as vitreous silica, a borosilicateglass, or an aluminosilicate glass. In some instances, the material ofthe dielectric body 102 is an oxide material such as magnesium oxide(e.g., MgO), aluminum oxide (e.g., Al₂O₃), silicon dioxide (e.g., SiO₂),titanium dioxide (e.g., TiO₂), zirconium dioxide, (e.g., ZrO₂), yttriumoxide (e.g., Y₂O₃), lanthanum oxide (e.g., La₂O₃), and so forth. Theoxide material may be non-stoichiometric (e.g., SiO_(x)), and may alsobe a combination of one or more binary oxides (e.g., Y:ZrO₂, LaAlO₃,etc.). In certain variations, the combination may correspond toBaLn₂Ti₄O₁₂ where Ln refers to one or more elements from the lanthanidegroup of the periodic table of elements. In other instances, thematerial of the dielectric body 102 is a non-oxide material such assilicon (Si), diamond (C), gallium nitride (GaN), calcium fluoride(CaF), and so forth.

The dielectric body 102 additionally includes an elongated slot 114through the region 112 extends from a slot opening in a surface of thedielectric body 102 at least partially through the dielectric body. InFIG. 1A, the elongated slot 114 extends completely through dielectricbody 102 to a second slot opening. The array of cavities 108 and theelongated slot 114 define a waveguide having a waveguide mode. Duringoperation, the waveguide may direct radio frequency (RF) electromagneticradiation (or waves thereof) along an axis of the region 112, such astowards an end of the dielectric body 102.

The example photonic crystal maser 100 also includes a vapor (or asource of the vapor) in the elongated slot 114. The vapor may includeconstituents such as a gas of alkali-metal atoms, a noble gas, a gas ofdiatomic halogen molecules, or a gas of organic molecules. For example,the vapor may include a gas of alkali-metal atoms (e.g., K, Rb, Cs,etc.), a noble gas (e.g., He, Ne, Ar, Kr, etc.), or both. In anotherexample, the vapor may include a gas of diatomic halogen molecules(e.g., F₂, Cl₂, Br₂, etc.), a noble gas, or both. In yet anotherexample, the vapor may include a gas of organic molecules (e.g.,acetylene), a noble gas, or both. Other combinations for the vapor arepossible, including other constituents. The source of the vapor maygenerate the vapor in response to an energetic stimulus, such as heat,exposure to ultraviolet radiation, irradiation by laser light, and soforth. For example, the vapor may correspond to a gas of alkali-metalatoms and the source of the vapor may correspond to an alkali-metal masssufficiently cooled to be in a solid or liquid phase when disposed intothe elongated slot 114.

In many implementations, the vapor has electronic transitions that aredefined between pairs of electron energy levels (e.g., a Rydbergtransition, an atomic transition, a molecular transition, etc.). Inparticular, the vapor includes one or more input electronic transitionsand an output electronic transition coupled to the one or more inputelectronic transitions. The output electronic transition is operable toemit a target RF electromagnetic radiation and is resonant with one ormore waveguide modes of the waveguide. Examples of electronictransitions are described further in relation to FIG. 2. In someimplementations, the example photonic crystal maser 100 includes a laser(e.g., a pump laser) configured to generate an optical signal capable ofexciting the one or more input electronic transitions of the vapor.However, other energy sources are possible (e.g., a source ofradio-frequency photons). In some implementations, the output electronictransition is operable to emit a target RF electromagnetic radiationhaving a frequency in a range from 100 MHz to 1 THz.

The photonic crystal structure 110 may define a photonic band gap forthe target RF electromagnetic radiation in the waveguide. The photonicband gap may be for a transverse magnetic (TM) mode, a transverseelectric (TE) mode, or both, of the target RF electromagnetic radiationin the waveguide. The photonic band gap may allow the photonic crystalstructure 110 to influence properties of the target RF electromagneticradiation. For example, the photonic crystal structure 110 may beconfigured to concentrate the target RF electromagnetic radiation in theelongated slot 114. The photonic crystal structure 110 may also beconfigured to decrease a group velocity of the target RF electromagneticradiation (or waves thereof) along a direction of the elongated slot 114(e.g., along an axis of the elongated slot 114). Such influence mayallow the photonic crystal structure 110 to control an absorption andemission of photons by the vapor. Examples of absorption and emissionare described further in relation to FIGS. 3A-5 and 7A-9D.

In some implementations, the elongated slot 114 extends partiallythrough the dielectric body 102 and the dielectric body 102 includes asurface defining a slot opening of the elongated slot 114. In theseimplementations, the example photonic crystal maser 100 includes anoptical window (e.g., optical window 104) that covers the elongated slot114 and has a window surface bonded to the surface to form a seal aboutthe slot opening. Such sealing may assist the optical window anddielectric body 102 in sealing the vapor (or the source of the vapor) inthe elongated slot 114, thereby defining a vapor cell within the region112. The optical window may be bonded to the dielectric body 102 using acontact bond, an anodic bond, a glass frit bond, and so-forth. Suchbonds may be formed using techniques described in U.S. Pat. No.10,859,981 entitled “Vapor Cells Having One or More Optical WindowsBonded to a Dielectric Body,” the disclosure of which, is incorporatedherein by reference in its entirety.

The optical window may be formed of a material that is transparent toelectromagnetic radiation (e.g., laser light) used to stimulate thevapor to emit the target RF electromagnetic radiation. For example, theoptical window may be transparent to infrared wavelengths ofelectromagnetic radiation (e.g., 700-5000 nm), visible wavelengths ofelectromagnetic radiation (e.g., 400-700 nm), or ultraviolet wavelengthsof electromagnetic radiation (e.g., 10-400 nm). Moreover, the materialof the optical window may be an insulating material having a highresistivity, e.g., ρ>10³ Ω·cm, and may also correspond to a singlecrystal material, a polycrystalline material, or an amorphous (or glass)material. For example, the material of the optical window may includesilicon oxide (e.g., SiO₂, SiO_(x), etc.), such as found within quartz,vitreous silica, or a borosilicate glass. In another example, thematerial of the optical window may include aluminum oxide (e.g., Al₂O₃,Al_(x)O_(y), etc.), such as found in sapphire or an aluminosilicateglass. In some instances, the material of the optical window is an oxidematerial such as magnesium oxide (e.g., MgO), aluminum oxide (e.g.,Al₂O₃), silicon dioxide (e.g., SiO₂), titanium dioxide (e.g., TiO₂),zirconium dioxide, (e.g., ZrO₂), yttrium oxide (e.g., Y₂O₃), lanthanumoxide (e.g., La₂O₃), and so forth. The oxide material may benon-stoichiometric (e.g., SiO_(x)), and may also be a combination of oneor more binary oxides (e.g., Y:ZrO₂, LaAlO₃, BaLn₂Ti₄O₁₂, etc.). Inother instances, the material of the optical window is a non-oxidematerial such as diamond (C), calcium fluoride (CaF), and so forth.

In some implementations, the surface of the dielectric body 102 definesa cavity opening for each of the array of cavities 108. The opticalwindow may or may not cover each of the cavity openings. Inimplementations where the optical window does cover each of the cavityopenings, the window surface of the optical window may form a seal abouteach of the cavity openings. In some implementations, the window surfaceof the optical window is a first window surface, and the optical windowincludes a second window surface opposite the first window surface. Insuch implementations, the example photonic crystal maser 100 may includea dielectric plate separated from the second window surface by a gap.The dielectric plate may be a plate body formed of dielectric material,such as described above in relation to the optical window. Thedielectric plate and its effects on a band edge of the photonic crystalstructure 110 are described further in relation to FIGS. 4A and 4B.

In some implementations, the elongated slot 114 extends entirely throughthe dielectric body 102. For example, as shown in FIG. 1A, thedielectric body 102 may include a first surface 116 opposite a secondsurface 118 and the elongated slot 114 extends through the dielectricbody 102 from the first surface 116 to the second surface 118. The firstsurface 116 may define a first slot opening 120 for the elongated slot114 and the second surface 118 may define a second slot opening (notshown) for the elongated slot 114. In these implementations, the examplephotonic crystal maser 100 includes first and second optical windows104, 106 covering, respectively, the first and second slot openings ofthe elongated slot 114. The first and second optical windows 104, 106each have a window surface bonded to the surface of the dielectric body102 and may seal the vapor (or the source of the vapor) in the elongatedslot 114 to define a vapor cell. In such cases, the first optical window104 may cover the first slot opening 120 and may have a first windowsurface 122 bonded to the first surface 116 of the dielectric body 102to form a seal about the first slot opening 120. Similarly, the secondoptical window 106 may cover the second slot opening and may have asecond window surface 124 bonded to the second surface 118 of thedielectric body 102 to form a seal about the second slot opening.

In implementations where the example photonic crystal maser 100 includesfirst and second optical windows 104, 106, the first and second surfaces116, 118 of the dielectric body 102 may define, respectively, first andsecond cavity openings for each of the array of cavities 108. In theseimplementations, the first and second optical windows 104, 106 may ormay not cover, respectively, each of the first and second cavityopenings. In implementations where they do, the first window surface 122may form a seal about each of the first cavity openings and the secondwindow surface 124 may form a seal about each of the second cavityopenings.

In some implementations, the example photonic crystal maser 100 includesan impedance-matching structure 126 configured to impedance match thetarget RF electromagnetic radiation to an ambient environment of thephotonic crystal maser 100. In these implementations, the region 112 inthe array of cavities 108 may extend along an axis 128 and the elongatedslot 114 may be aligned parallel to the axis 128 (e.g., be coincidentwith the axis 128). The dielectric body 102 then includes theimpedance-matching structure 126, which may extend from an end 130 ofthe dielectric body 102 and be aligned with the axis 128. Theimpedance-matching structure 126 may be an integral part of thedielectric body 102 but may also be a separate body. If separate, theimpedance-matching structure 126 may be formed of dielectric material.However, the impedance-matching structure 126 may also be a conventionalcoupler formed of metal. FIG. 1A shows the impedance matching structure126 as a protrusion from the dielectric body 102 that terminates in ataper. However, other geometries for the impedance-matching structure126 are possible.

In some implementations, the impedance-matching structure 126 iselectromagnetically coupled to an output mirror, such as a photoniccrystal mirror 132, to impedance match an output beam to a medium (e.g.,air) in which the output beam is intended to propagate. The photoniccrystal mirror 132 may be defined by one or more offset cavitiesspatially offset from an ideal periodic position in the array. The oneor more offset cavities may reside nearest an end of the elongated slot114 (e.g., end 130) and have respective spatial offsets away from theend of the elongated slot 114. The one or more offset cavities may alsoreside nearest a side of the elongated slot 114 and have respectivespatial offsets away from the side of the elongated slot 114. Otherlocations are possible. A lens may also be added to collimate the outputbeam. In some implementations, a polarizer may be added to theimpedance-matching structure 126 to filter a polarization of the outputbeams. For example, the impedance-matching structure 126 may terminatein a tapered end and include a narrow portion aligned with the taperedend. An array of co-planar segments may extend outward from the narrowportion and have a periodic spacing therealong. The array of co-planarsegments is configured to filter a polarization of the target RFelectromagnetic radiation.

In some implementations, the photonic crystal mirror 132 is placed atone or both ends of the elongated slot 114. FIG. 1A shows the case inwhich the photonic crystal mirror 132 is present at both ends of theelongated slot 114. The presence of the photonic crystal mirror 118 mayincrease the output power, may lower the gain threshold of the maser, orboth. For example, the photonic crystal mirror 132 may reflectelectromagnetic radiation that traverses the region 112 during operation(e.g., the target RF electromagnetic radiation emitted by the vaporduring operation of the example photonic crystal maser 100). In thiscapacity, the region 112 may serve as part of a maser cavity, such asthe interior of a maser cavity. Moreover, the photonic crystal mirror132 may assist the array of cavities 108 and the elongated slot 114 indefining a cavity structure (e.g., a slot waveguide) for electromagneticradiation emitted by the vapor.

In many variations, the photonic crystal mirror 132 corresponds to analteration in the dimensional characteristics of the photonic crystalstructure 110 near an end of the elongated slot 114. For example,transmission of the target RF electromagnetic radiation through thephotonic crystal structure 110 at the ends of the elongated slot 114 canbe altered by changing a spacing of cavities 108 in the array, athickness of the dielectric body 102, a diameter of the cavities 108 inthe array, and so forth. It will be appreciated that, in the dielectricbody 102, a perfect photonic crystal geometry for the target RFelectromagnetic radiation (or resonant wave) may act as a perfectreflector, while the absence of the photonic crystal may act as aperfect transmitter.

In some implementations, the photonic crystal mirror 132 is configuredwith a reflectivity greater than 80% for frequencies of electromagneticradiation at or near a cavity resonant frequency, ω_(c), of the photoniccrystal structure 110. This reflectivity may increase a cavity qualityfactor, Q, associated with the photonic crystal structure 110 (or region112 therein), thereby lowering a threshold condition for masing to takeplace. The threshold condition for masing is discussed further below inrelation to Eqs. (1)-(2). In some variations, the reflectivity isgreater than 85%. In some variations, the reflectivity is greater than90%. In some variations, the reflectivity is greater than 92%. In somevariations, the reflectivity is greater than 94%. In some variations,the reflectivity is greater than 96%.

In some implementations, an optical mirror 134 is placed at one or bothends of the elongated slot 114. The optical mirror 134 may be angledrelative to an optical pathway defined by the elongated slot 114, oralternatively, be angled perpendicular to the optical pathway. Theoptical mirror 134 may serve to guide optical signals along alongitudinal axis of the elongated slot, such as axis 128. To do so, theoptical mirror 134 may include surfaces configured to reflect suchoptical signals. The optical signals may include light received into theelongated slot 114 from the laser.

In some implementations, the vapor is a vapor of atoms in which eachatom can function as an emitter. During operation, the photonic crystalstructure 110, which surrounds the elongated slot 114, may slow andconcentrate an electromagnetic wave at an atomic transition frequency ofthe atoms. The atoms are pumped with the laser(s) so that a populationinversion is established on an atomic u→l transition, which is resonantwith a resonant mode (or waveguide mode) of the waveguide. Emission ofradiation into the resonant mode of the waveguide can be enhancedbecause the electric field is stronger, favoring emission. Stimulatedemission dominates, creating a coherent directed maser beam along thewaveguide that can be impedance matched and shaped for free-spacepropagation. Photonic crystal mirrors can be implemented at the ends ofthe elongated slot 114 so the radiation can propagate back and forth inthe elongated slot 114 and be further amplified. The elongated slot 114takes the energy stored in the population inversion and causes it to beemitted into the waveguide mode resulting in a coherent, directed beamof radiation. Analogous operation is possible for implementations of theexample photonic crystal maser 100 in which the vapor is a vapor ofmolecules.

The example photonic crystal maser 100 may be constructed in a mannersuitable for mass production. The example photonic crystal maser 100 mayalso be combined with a Rydberg atom receiver, Rydberg atom vapor cellsensor, or array of Rydberg atom vapor cell sensors to create devicesthat can receive and transmit RF radiation. The amount of poweroutputted by the example photonic crystal maser 100 may be controlled toextraordinarily low levels by changing an intensity of the laser.Moreover, the switching time may be nanoseconds because cavity lifetimescan be on this scale (see also description relation to Eq. (6)). Becauseof the nanosecond lifetimes and the ability to modulate the laser at GHzbandwidths, modulating the laser can imprint baseband modulations on thecarrier frequency on the same frequency scale (e.g., GHz).

Although FIG. 1A depicts the example photonic crystal maser 100 ashaving a linear region 112 and a linear elongated slot 114, othergeometries are possible. For example, FIG. 1B presents a schematicdiagram, in top view, of the example photonic crystal receiver 100, butin which dielectric body 102 includes a ring resonator structure. Inparticular, the region 112 forms a loop (e.g., an elliptical loop) inthe array of cavities 108. In many variations, the loop is a closedloop, such as circle, an ellipse, an oblong, and so forth. The elongatedslot 114 extends along a loop axis (e.g., an elliptical axis) of theloop to form a looped slot 150 (e.g., an elliptical slot). All or aportion of the looped slot 150 may be partitioned off (e.g., bytransparent walls, lenses, mirrors, etc.) to contain the vapor or thesource of the vapor. FIG. 1B shows the case in which a portion 152 ofthe looped slot 114 contains the vapor or the source of the vapor. Insome variations, such as shown in FIG. 1B, the array of cavities 108forms a loop. However, other distributions are possible for the array ofcavities 108.

The looped slot 150 may be associated with first and second loopdirections 154, 156 along the loop axis, with the first loop direction154 being opposite the second loop direction 156. In theseconfigurations, the looped slot 150 includes first and second RF ports158, 160. First and second directional couplers 162, 164 are coupled to,respectively, the first and second RF ports 158, 160. The firstdirectional coupler 162 is configured to receive a first portion of thetarget RF electromagnetic radiation traveling along the first loopdirection, and the second directional coupler 164 is configured toreceive a second portion of the target RF electromagnetic radiationtraveling along the second loop direction. In many variations, the firstdirectional coupler 162 is more strongly coupled to the looped slot 150than the second directional coupler 164.

A looped configuration for the region 112 and elongated slot 112 maybring some advantages over a linear configuration in certain cases. Forexample, the linear configuration allows the target RF electromagneticradiation, when emitted, to travel principally along two oppositedirections, such as along a linear axis of the elongated slot 114.During such travel, the target RF electromagnetic radiation may beamplified by interacting with the vapor, which can operate as a gainmedium. However, this dual-direction travel may also allow photonsassociated with the traveling target RF electromagnetic radiation—e.g.,waves of photons traveling forwards and backwards in the elongated slot114—to interfere with each other and establish a standing wave of thetarget RF electromagnetic radiation in the elongated slot 114. Thisstanding wave is associated with a series of minimum and maximum fieldintensities along a length of the elongated slot 114. The minimums mayresult little to no stimulated emission at some portions of the vaporwhile the maximums may saturate the emission at other portions. Themaximums may be particularly undesirable if their electromagnetic fieldenergy is greater than can be absorbed by the vapor at their locations.As a result, the standing wave of target RF electromagnetic radiationmay not efficiently use the vapor in the elongated slot 114. The targetRF electromagnetic radiation may saturate the output power at lowermagnitudes of field strength than if all the vapor were used.

In contrast, the looped configuration can, in certain cases, moreefficiently use the vapor by incorporating directional couplers andestablishing a traveling wave of the target RF electromagneticradiation. For example, a high-efficiency directional coupler (e.g.,first directional coupler 162) may serve as a unidirectional device atthe first RF port 158 of the looped slot 150 and a low-efficiencydirectional coupler (e.g., second directional coupler 164) can be usedas an output coupler at the second RF port 160 of the looped slot 150.In the looped configuration, first photons circulating in the first loopdirection 154 (e.g., a clockwise direction) are coupled out of thelooped waveguide with low-efficiency and second photons circulating inthe second loop direction 156 (e.g., a counterclockwise direction) arecoupled out of the cavity with high efficiency. The loss of the secondphotons is designed to be enough that second photons, when interactingwith the vapor, do not reach the masing threshold. In contrast, thefirst photons are strong enough so that, when interacting with thevapor, the first photons extract all the energy from the gain medium. Inthis situation, the target RF electromagnetic radiation forms atraveling wave (especially in the vapor) and the entire vapor cantherefore be used as a gain medium to provide energy for masing.Moreover, the traveling wave allows the vapor to be selectivelyconstrained within a portion of the looped slot 150. An entire volume ofthe looped slot 150 need not be filled with the vapor. The portion maybe selected in length and position to maximize a participation of thevapor in stimulated emission.

Now referring to FIG. 2, a schematic diagram is presented of exampleenergy levels for a Rydberg atom maser, such as for the example photoniccrystal maser 100 of FIGS. 1A and 1B. The coefficients, A_(ij), areEinstein A coefficients. The wavy arrows show radiative decay pathwayswhile the solid arrows show excited transitions induced by lasers (orpump lasers). In FIG. 2, two excitation pathways are depicted. However,the lasers do not have to be resonant with the two-photon process (ortwo excitation pathways). Single photon or other types of multi-photonexcitations are also possible. In such cases, the allowed transitionschange because the parity of the two states involved in any dipoletransition must change during excitation or decay. The energy levels uand 1 are Rydberg states in cases where the vapor consists of atoms.

The laser creates a population inversion on a transition of the emitterslocated in a waveguide of the photonic crystal structure (e.g., a vaporin an elongated slot residing within the photonic crystal structure). InFIG. 2, a portion of the population of emitters is pumped to level u,creating an inversion on the u→l transition. Most of the populationresides in state g. The decay from u→i and i→g corresponds to spectatortransitions as these decays, the detuning of the lasers from i, and theRabi frequencies of the near-resonant lasers determine the population inu. A two-photon excitation scheme consistent with Rydberg atom-sensingis shown in FIG. 2, since the sensing lasers can also be used to pumpthe maser in situations where a signal source and a receiving sensor areneeded. Single photon or other multi-photon pumping schemes may also beimplemented. For the pumping scheme to work, which may include creatingan inversion on the u→l transition, the magnitude of A_(ul) should beless than A_(lg) (i.e., A_(ul)<A_(lg)) and preferably much less thanA_(lg) (i.e., A_(ul)<<A_(lg)). In the case of gaseous atoms, thetransition u→l is a Rydberg transition, so its frequency is in the RFband. The photonic crystal and waveguide are designed to be resonantwith the RF transition u→l. For the example energy levels shown in FIG.2, energy levels i and l have the same parity. Moreover, energy levels uand g have the same parity. It will be appreciated that spontaneousemission or dipole coupling between energy levels requires a change inparity.

In many variations, the photonic crystal structure and elongated slotare configured to be resonant with the u→l transition. In thesevariations, the electromagnetic field associated with the resonant RFtransition (or output electronic transition of the vapor) is enhanced inthe photonic crystal structure, and especially in the elongated slot.This enhancement may increase the radiation rate into the associatedwaveguide mode relative to others (e.g., those at the same frequency orfrom competing transitions). The combination of the holes (or cavities)in the photonic crystal structure and the elongated slot in thedielectric body may define a waveguide. As such, the slowing due to thephotonic crystal structure and the concentration of the electromagneticfield in the elongated slot can operate in tandem to modify theradiation field so that the vapor located in the elongated slot is morelikely to radiate into the waveguide mode of the waveguide. Thewaveguide may be designed such that the waveguide mode is matched to theradiance (or emission) of the vapor. The radiation is linearly polarizedto couple to the waveguide. The enhanced coupling lowers the thresholdgain for masing action to occur. Once emission into the masing modebegins it is amplified by stimulated emission on the resonant transitioncausing the vast majority (or all) of the energy stored in the upperlevel, u, to be emitted coherently into the waveguide mode of thewaveguide.

Now referring to FIG. 3A, a contour map of an electric field magnitudeis presented for an example photonic crystal maser that has a resonantfrequency of 81.8 GHz. The contour map extends through a mid-planeparallel to the top surface of the example photonic crystal maser andincludes a slot waveguide therein. The contour map represents atime-averaged magnitude of the electric field in response to a simulateddipole oscillating at the resonant frequency of the example photoniccrystal maser. The polarization of the simulated dipole is normal to thetop surface. The inset of FIG. 3A provides a magnified view of thecontour map showing a magnitude of the electric field proximate acentral portion of the slot waveguide. Due to the normal orientation ofthe simulated dipole, the dipole is poorly coupled to the photoniccrystal maser mode as indicated by the small, concentrated magnitude ofthe electric field in the central portion of the slot waveguide. FIG. 3Bpresents the contour map of FIG. 3A, but in which the scale is increasedby 1000. FIGS. 3C-3E present the counter map of FIG. 3A at differentoscillation frequencies of the simulated dipole, but in which theorientation of the dipole is oriented parallel to the top surface andperpendicular to the slot walls. In this orientation, the dipole isstrongly coupled to the example photonic crystal maser. Theelectromagnetic field is enhanced and the emission of the dipole, whenon resonance, is strongly coupled to the photonic crystal structure,such as shown in FIG. 3D. Slightly off resonance, there is still somecoupling into the photonic crystal maser mode, such as shown in FIG. 3Aand FIG. 3B, but this coupling is weaker due to the frequency mismatchbetween the emission frequency and the resonant mode of the photoniccrystal maser.

Photonic crystal cavities and structures are ideal for integrating withvapor cells using contact bonding and machining methods, such asdescribed in U.S. Pat. Nos. 10,859,981 and 11,137,432. A photoniccrystal structure that acts as a concentrating element for MHz-THzelectromagnetic radiation can have cavities machined in it using lasers(e.g., a Protolaser R laser mill), mechanical machining, or deepreactive ion etching (DRIE). The cavities may be subsequently filledwith a vapor (e.g., a gas of alkali atoms) and sealed with opticalwindows to define a vapor cell. The photonic crystal structures can bedesigned to concentrate and bunch the incident high frequency electricfield in the vapor. Slowing down and concentrating the RF radiationfield in the vapor cell increases the radiation rate of atoms in theelongated slot into the waveguide mode of the waveguide.

For example, FIG. 4A presents a schematic diagram of a cross-section ofan example photonic crystal maser that has an optical window and amovable dielectric plate positioned above the optical window. Themovable dielectric plate (e.g., a movable glass plate, a sapphire plate,etc.) may be used to control a band edge of the example photonic crystalmaser. The band edge may be used to slow an RF radiation field along theexample photonic crystal maser. FIG. 4B presents a graph of the bandedge, showing how a position of the movable dielectric plate shifts afrequency position of the band edge. In particular, the graph shows howthe band edge shifts with a magnitude of a gap between the movabledielectric plate and an optical window of the example photonic crystalmaser. The moveable dielectric plate can be positioned precisely with amechanical screw, which may also be formed of a dielectric material.However, other positioning means are possible. In some instances, theexample photonic crystal maser includes two instances of the movabledielectric plate, one positioned above each of the two optical windows.

In another example, FIG. 5 presents a contour map of an electric fieldmagnitude through a cross-section of an example photonic crystalstructure. The cross-section includes the elongated slot, which isdefined by angled walls. FIG. 5 shows angled walls at angles of α=0°,2°, 4°, 6°, 8°, and 10°. However, other angles are possible. The higherwall angles, such that the cross-sectional shape resembles an“hourglass,” concentrate the field more in a gap of the elongated slot.The electric field can be increased in magnitude by greater than 10times. For α=10°, FIG. 5 shows an increase of about 30 times over thefree electric field.

In some implementations, the photonic crystal maser is based on highdielectric constant materials, such as silicon. These high dielectricconstant materials may be contact bonded using processes described inU.S. Pat. Nos. 10,859,981 and 11,137,432. Other high dielectricmaterials such as BaLn₂Ti₄O₁₂ (BLT) can also be used, for example, ifadhesion layers are applied. Contact bonding, anodic bonding, or othertypes of bonding may be used to construct a photonic crystal structureintegrated with a vapor cell to create a maser that can output coherentRF electromagnetic radiation. This construction will result in a maserthat is fully dielectric and can be integrated with other Rydbergatom-based sensing technologies. For example, the maser may beintegrated with Rydberg atom-based sensing technologies for testing inanechoic chambers where signal reception and transmission are bothrequired. Moreover, the maser can enable hetero- and homo-dyning forRydberg atom sensors with all-dielectric structures, allowing for moreelaborate signal processing strategies and phase detection methods.Silicon and glass can be machined using lasers to allow features inthese materials with 10 μm precision and 10's of μm sizes. Suchdimensional scales are ideal for photonic crystal masers where thephotonic crystal structure interacts with RF electromagnetic radiation,since the wavelength of such radiation is much greater than 10 μm.

The use of Rydberg atoms for electrometry can allow accurate andabsolute measurements of high frequency (GHz-THz) electric fields (e.g.,accurate to about 1 μV cm⁻¹). The calculated atomic shot noise limit inthe 5-25 GHz range can be about pV cm⁻¹ Hz^(−1/2), for standardinteraction volumes, determined by the number of participating atoms andthe coherence time. The sensitivity limits may be determined by shotnoise in the classical readout field. However, Rydberg atom electrometryis primarily used to measure RF electromagnetic fields. For applicationsin test and measurement and communications it is advantageous to have asource of RF radiation based on the same technology. For example, adielectric source of RF electromagnetic radiation can be used in testchambers without perturbing the environment. Coupled with Rydbergatom-based sensors, a fully dielectric over-the-air test and measurementsystem can be setup in a test chamber, increasing accuracy anddecreasing the size of the test chamber, consequently reducing cost.

The photonic crystal maser can be used for test and measurement,communications, spectroscopy, timing and referencing frequency.Advantages of the photonic crystal maser may include one or more of thefollowing: [1] an all-dielectric construction that minimizesinterference with other nearby devices; [2] masing action that takesplace with vapor (e.g., thermal atoms) in a vapor cell; [3] adirectional emission that spreads minimally as it propagates; [4] anability to be combined as a source with Rydberg atom-based sensingtechnologies. The source can be used for advanced signal processing(mixing strategies), as a signal source in one-box testers, and as adirectional communications device; [5] a lightweight, portableconfiguration that may be less costly than traditional masers. Theconfiguration is based on diode laser technology and vapor celltechnology. The same lasers that are used for detection (sensing) mayalso be used to pump the photonic crystal maser; [6] a construction thatcan be manufactured more easily than glass blown structures and may alsobe more robust; [7] an ability to act as an amplifier for Rydbergatom-based receivers. The photonic crystal maser can be integrated intothe receiver, for example, as a first stage, or preamp, to increase thesignal; [8] an extremely low gain threshold, which can be used toproduce low power precisely, thus allowing applications in testing; [9]because of the low masing threshold, the cavity lifetime can be smallenabling the output power to be modulated with a high bandwidth (GHzbaseband modulation). Such modulation can be achieved by modulating oneor more pumping lasers; [10] linearly-polarized output; [11] pulsed andcontinuous-wave operation; [12] operation over a broad frequency span,such as from 100 MHz-1 THz. Other advantages are possible.

In some implementations, the photonic crystal masers described hereinmay operate according to the following principles. For example, theaverage photon number per unit time in the photonic crystal cavity (orelongated slot in a photonic crystal structure) may be represented byEq. (1):

$\begin{matrix}{\left. {\frac{d\left\langle {n(t)} \right\rangle}{dt} = {{\left( {A - \frac{\omega}{Q}} \right)\left\langle n \right\rangle} + A - {B\left\langle n^{2} \right\rangle} + {2\left\langle n \right\rangle} + 1}} \right){{{where}\mspace{14mu} A} = {{2{r_{a}\left( \frac{g}{\gamma} \right)}^{2}\mspace{14mu}{and}\mspace{14mu} B} = {4{A\left( \frac{g}{\gamma} \right)}^{2}}}}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$Here, Q is the cavity quality factor, ω is the maser angular frequency,

n²

is the average photon number squared in the cavity of the photoniccrystal maser (related to the photon number fluctuations), and

n

is the average number of photons in the cavity. The cavity resonantfrequency, ω_(c), is assumed in resonance with the masing transition,ω_(c)=ω. As such,

n²

and

n

may be calculated using a density matrix for the system. In thevariables A and B, g is the atom-field coupling constant in the cavity,γ is the decay rate of upper state and r_(a) is the number of atomsentering the cavity per second. In steady state, r_(a) is also thenumber of atoms leaving the laser atom interaction region per second.The average number of photons in the cavity may be represented by Eq.(2) in steady state:

$\begin{matrix}{{\overset{\_}{n}}_{ss} = {\frac{AQ}{\omega} \times \frac{\left( {A - \frac{\omega}{Q}} \right)}{B}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$Eq. (2) provides insight into the difference between maser operation andreceiver operation. When A>ω/Q the atoms will emit coherently, thenumber of photons in the cavity will grow and there will be masing,i.e., A>ω/Q is the threshold condition for masing. If A<ω/Q then thesystem is in the regime of receiver operation. For example, the Q of areceiver is 1 if the structure has no mirrors, Q˜10¹² Hz, and A˜10¹⁰,making AQ/ω˜10⁻². For the photonic crystal maser above threshold, thesteady-state average number of photons can be approximated usingEquation (3),

$\begin{matrix}{{\overset{\_}{n}}_{ss} \approx \frac{A^{2}Q}{B\omega}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$The energy stored in the cavity may be determined by the number ofphotons according to,E _(ss) =ℏωn _(ss)  Eq. (4)and the power emitted from the photonic crystal maser may be given by,

$\begin{matrix}{P_{ss} = \frac{E_{ss}}{\tau_{c}}} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$where τ_(c) is the lifetime of the photon in the cavity. Q, ω_(c), andτ_(c) are all related because they are determined by the properties ofthe cavity. Ultimately, these properties depend on the reflectivity ofthe mirrors and losses in the cavity (or elongated slot). The cavity maybe assumed to be on resonance so ω=ω_(c). However, solutions foroff-resonance are also possible. The cavity Q can be related to thecavity resonant frequency, ω_(c)=ω, and the linewidth of the cavity,Δω_(c)=τ_(c) ⁻¹ as shown by Eq. (6):

$\begin{matrix}{Q = {\frac{\omega_{c}}{\Delta\omega_{c}} = {\omega_{c}\tau_{c}}}} & {{Eq}.\mspace{14mu}(6)}\end{matrix}$If Δω_(c) and ω_(c) are measured, then Q can be determinedexperimentally, which similarly determines τ_(c), since it is theinverse of Δω_(c). The reflectivity of the cavity mirrors and estimatesof cavity loss can be used to choose a Q for a particular design. Thiscan be seen in Eqs. (7) and (8),Δω=cα _(r)  Eq. (7)where α_(r) is the loss coefficient in the cavity,

$\begin{matrix}{\alpha_{r} = {\alpha_{s} + {\frac{1}{2d}\ln\frac{1}{R_{1}R_{2}}}}} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$and c is the speed of light. In Equation (8), α_(s) is the cavity lossand d is the cavity length. R₁ and R₂ are the cavity mirrorreflectivity. From these relations, assuming the photonic crystal maseris well above threshold, γ≈g, and that the atom-field coupling hasreached the decay constant of the lower state, i.e., saturation, anequation may be derived for the power,

$\begin{matrix}{P_{ss} \approx \frac{\hslash r_{a}\omega}{2}} & {{Eq}.\mspace{14mu}(9)}\end{matrix}$Eq. (9) for P_(ss) may be interpreted in a straightforward manner and isconsistent with other formalisms for finding maser power. Eq. (9) mayrepresent an operation condition where, at saturation, each atom passingthrough the cavity emits a photon into the cavity. Therefore, the poweris determined by the number of active atoms per unit time. This model isconsistent with the fundamental operation of a maser, which is tochannel the emission of all the atoms into a single mode of theelectromagnetic field.

For a Rydberg atom density of 10¹⁰ cm⁻³, just below the density wherecollisions will become significant (not necessarily a limiting factorbut perhaps requiring more pump power), a transit time limited rater_(a) of 200 kHz (atoms hit the walls at this rate and are destroyed,but a new atom is excited in the interaction region via the pumplasers); a 100 GHz transition; and a 0.157 cm³ cylindrical pumped atomicvolume, corresponding to a 20 cm length and 1 mm diameter interactionregion, the photonic crystal maser can produce a power of around 10 nW(−50 dBm). The maser output is polarized parallel to the elongated slot,i.e., parallel to the slab plane of the photonic crystal structure. Thesteady-state density of Rydberg atoms, 10¹⁰ cm³, is straightforward toproduce. Higher powers are possible by increasing the number of atomsand/or the saturation rate. Although this number may be small comparedto an antenna, it is significant for testing applications and is a largesignal for testing a device's receiving capability. More importantly,the radiation is coherent and directional (e.g., does not spread as thesquare of the distance). At 100 GHz, a Q=1000 gives a cavity lifetime ofτ_(c)˜1 ns. Consequently, the pump lasers can be modulated at highfrequency to put large (GHz) bandwidth baseband modulation on the maseroutput. The ability to produce coherent, directed radiation in anall-dielectric package, with large modulation bandwidth at extremely lowpowers to test devices precisely is advantageous.

The photonic crystal maser can, in some implementations, be configuredto have extremely low threshold powers. For example, the gaincross-section on resonance may be represented by Eq. (9):

$\begin{matrix}{\sigma_{ul}^{r} = {{\sqrt{\frac{\ln(2)}{16\pi^{3}}} \times \frac{\lambda_{ul}^{2}A_{ul}}{n^{2}\Delta v}} \approx {{10^{- 5}} - {10^{- 6}\mspace{14mu}{cm}^{2}}}}} & {{Eq}.\mspace{14mu}(10)}\end{matrix}$As shown by Eq. (10), the magnitude of the gain cross-section may bevery high. Moreover, the corresponding saturation intensity may beunusually small, as shown by Eq. (11):

$\begin{matrix}{I_{sat} = {\frac{\hslash\omega}{\sigma_{ul}^{r}\tau_{u}} \approx {{10^{- 9}} - {10^{{- 1}0}{W \cdot m^{- 2}}}}}} & {{Eq}.\mspace{14mu}(11)}\end{matrix}$This value shows that the threshold for masing is very small, allowingfor low power operation. Here, Eq. (10) and Eq. (11) use parametersconsistent with those of the prior example: λ_(ul)˜0.22 cm; A_(ul)˜50kHz; Δω ˜2π×100 kHz; determined by transit time broadening and wallcollisions, ω˜2π×100 GHz; and τ_(u)˜5 μs.

If u is a Rydberg state and the atom is in free-space, the radiativedecay from u may be dominated by decay to the lowest allowed statebecause of the ω³ dependence of the spontaneous emission rate, A_(ui),A_(lg)˜20 kHz. Typically, A_(ul)˜20 Hz. Similar spontaneous emission andblack-body induced transition rates normally lead to population of otherenergetically nearby Rydberg states. The condition for effective pumpingto state u, A_(ul)<<A_(lg), is automatically fulfilled given theseconsiderations. However, leakage due to transitions other than u→l maycause the population in these states to disperse amongst a host ofdifferent atomic Rydberg states. The addition of the photonic crystalstructure, shown in FIG. 3D and FIG. 5, mitigates other competingtransitions removing the population from u by changing theelectromagnetic mode structure. The photonic crystal structure,comprising the elongated slot, the array of cavities, and the alteredarray of holes forming the mirrors at each end of the elongatedstructure, increases the radiation rate into the cavity mode (orwaveguide mode) which is energetically the same (in resonance with) theu→l transition. The photonic crystal structure can increase the rate ofemission on the u→l transition by greater than a thousandfold even inthe absence of large amounts of stimulated emission caused by thebuild-up of photons in a cavity. This increase means that A_(ul) for theatoms contained in the elongated slot is about 20 kHz. Consequently,emission is largely confined to the u→l transition. The u→i transitionshown in FIG. 2 has similar magnitude but can be saturated by thepumping lasers. For example, the pump laser Rabi frequencies must belarge enough to maintain a population in u so there is an inversion onthe u→l transition. The pump lasers must have an effective Rabifrequency greater than A_(ul) to saturate the population in u. Theserequirements are straightforward to achieve in beam, vapor cell, andcold atom experiments. The system is effectively a two-level systemconsisting of the u and l states. FIGS. 3C-3E show that only a dipoleoriented to the photonic crystal mode can couple effectively into thephotonic crystal structure. The maser emission, then, will be linearlypolarized and the u→l transitions will be vertical transitions, Δm=0.

In a free space description, the photonic crystal maser would saturatewhen the emission rate u→l in the masing cavity (e.g., the elongatedslot) reached the decay rate of l, dominated by spontaneous emission, ofabout 20 kHz. The saturation of the emission rate occurs when thepopulation in the u an l states become approximately equal thusdestroying the population inversion. The saturated emission rate can beincreased due to effects such as collisions and transit time broadening(atoms passing through the active region of the gain medium). In thecase of the photonic crystal maser, the loss rate of atoms in both the uand the l states is dominated by collisions of the atoms with the walls,˜100-200 kHz, depending on the slot dimensions. Although, the wallcollisions can have a negative effect on the u state population, makingit more difficult to establish the inversion on the u→l transition, theeffect may be compensated by pumping the photonic crystal maser harder.Once the atoms bounce off the walls they are ‘recycled’ into the beamand can be excited again by the pump lasers. The described effect is notsubstantially different than maser experiments carried out with anatomic beam, where the atoms passed through the cavity and the decayrate was inversely proportional to the transit time through the cavity.These effects are taken into account in the estimates above of maserpower.

Pump light can be channeled along the gain media, the atomic sample inthe slot, by fiber coupling to a turning mirror located in the slot.FIG. 6A presents a schematic diagram, in perspective and top views, ofan example photonic crystal maser that is being optically pumped by alaser. The top portion of FIG. 6A is shown in the perspective viewwhereas the bottom portion of FIG. 6A presents the top view. A path of abeam from the laser is represented by a dashed line. A mirror on theopposite end of the elongated slot can reflect the light back along theelongated slot to increase the pumping efficiency or direct thereflected light onto a non-reflecting surface. A turning mirror sits ina cut-out at one end of the slot and the light can be directed withmirrors along the length of the slot. Smaller coupling optics than thoseshown in FIG. 6A can be used to minimize the perturbation of the maserfield. For example, FIGS. 6B and 6C present schematic diagrams of theexample photonic crystal maser of FIG. 6A, but in which miniaturecoupling optics are used to direct light from a pump laser into theexample photonic crystal maser. The pump light may be polarized tooptimize the inversion on the masing transition. Such polarization, may,for example, limit population on the stretched states if the angularmomentum of u is larger than I.

The angular spread of the beam is small compared to an antenna whichalso must be considered when comparing the output power of the twodevices (i.e., the photonic crystal maser versus the antenna). Theoutput of the antenna spreads with propagation distance proportionallyto R², with intensity decreasing as R⁻². The beam of the photoniccrystal maser can be made to propagate as a collimated beam. A sourcespreading out from an antenna, will decrease by roughly 6 orders ofmagnitude after 1 km of propagation in comparison to a collimated beam.A photonic crystal maser with −50 dBm of output power is roughlyequivalent to a 10 dBm antenna source at 1 km. This difference isadvantageous for point-to-point communications systems since the powercan be low and directional. Coupled with a photonic crystal receiver, apoint-to-point, secure communications system can be constructed thatuses exceptionally low power, i.e., a Rydberg atom transceiver.Moreover, the output of the photonic crystal maser can be coupled tofree space with an antenna structure (or impedance matching structure),as shown in FIG. 1A, or collimated with a lens or a combination thereof.Part of the output coupling structure (e.g., a taper) can include apolarizer.

Tuning of the resonant structure to the masing wavelength can be done inseveral ways. An example is shown in FIGS. 4A-4B. In FIGS. 4A-4B, apiece of thin glass is moved some distance from the photonic crystalmaser to change the effective dielectric constant of the region wherethe masing wave propagates. FIGS. 4A-4B show a single glass piece but asymmetric structure with a glass piece on each side of the photoniccrystal structure can also be used. Various positioning mechanisms, suchas a screw made of dielectric material or piezoelectric positioning (ifsome metal can be tolerated in an application) can be used to positionthe tuning elements. The positioning screws can be remotely motorizedusing a drive mechanism. Other tuning mechanisms are possible. Forexample, tuning can also be done using similar screw and piezoelectricelements. Likewise, the elongated slot can be cut in two or more piecesand the length of the overall structure can be adjusted to put thedevice into resonance.

A calculation of a radiation enhancement factor, β, is shown in FIGS.7A-7B. FIG. 7A presents a schematic diagram, in perspective view, of anexample photonic crystal structure used to determine the enhancementfactor for a radiating dipole. The radiating dipole couples into theresonant mode of the example photonic crystal structure. FIG. 7Bpresents a graph of the enhancement factor simulated for the examplephotonic crystal structure of FIG. 7A. The enhancement factor issimulated versus frequency and corresponds to the increase in radiationrate A_(ul) inside the example photonic crystal structure,A_(eff)=βA_(ul). The example photonic crystal structure is the same asfor the example photonic crystal maser of FIGS. 3A-3E but does not havemirrors in order to determine the enhancement factor for this particularconfiguration. The peak enhancement is about 365 for this configuration,meaning that the radiation rate inside the photonic crystal structure is365 A_(ul). FIG. 7B also shows significant enhancement off resonance(e.g., about 100).

In FIGS. 7A-7B, the example photonic crystal structure used for thesimulation has the same photonic crystal spacing, hole size andthickness of a maser design, but has no mirrors and is symmetric. Thesymmetry and lack of mirrors allow the enhancement factor, due to theslowing and concentration of the RF electric field, to be extracted fromthe simulations. FIG. 7B shows an enhancement factor β=365 at resonance.If A_(ul)=20 Hz for the masing transition and the photonic crystalstructure is resonant with the u→l transition, then the radiation ratein the photonic crystal, A_(eff), can be 7 kHz. There is also asignificant enhancement of about 100 to the blue side of the band edge.The band edge is shown on the red side of the resonant feature in FIG.7B where the response is zero. FIGS. 7A-7B indicate that the radiationrate enhancement is sufficient to make the spontaneous emission rate onthe u→l transition dominate the decay over transitions to other modes,which are non-resonant with the photonic crystal structure. Thisdominance is due to the slowing of the electromagnetic wave and theconcentration of the electric field in the photonic crystal structure.

FIG. 8 presents a table of example design parameters for a photoniccrystal maser. The design parameters correspond to different targetfrequencies of electromagnetic radiation. The design parameters includea slab thickness, a hole diameter, and a lattice constant for the array.In this set of designs the holes are all circular. However, other holeshapes can be used. Moreover, this set of design parameters correspondsto a silicon frame. However, design parameters for other frames arepossible (e.g., a sapphire frame, a BLT frame). In some variations, asize of the elongated slot may be altered as well. For example, theelongated slot may fit into the slab as a line defect that is about 3-6lattice constants long.

FIG. 9A presents a schematic view, in top view, of an example photoniccrystal structure having cavities configured to define a photoniccrystal mirror proximate an end of an elongate slot. The photoniccrystal mirror may be partially reflecting. In many variations, such asshown in FIG. 9A, the cavities are holes. By altering the size of theholes proximate the end of the elongated slot, the transmission of thetarget electromagnetic wave passing through the section of the photoniccrystal directly opposite the end can be altered. This alteredtransmission may be used to tune a reflectivity proximate the end,thereby creating the photonic crystal mirror. The reflectivity of thephotonic crystal mirror can vary over a broad range of reflectivity. InFIG. 9A, the altered region of the photonic crystal structure has beenextended away from the elongated slot to decrease the leakage throughthe photonic crystal mirror.

FIGS. 9B and 9C present contour graphs of electric field patterns thatcorrespond to a 97.8% and an 88.5% reflection from the photonic crystalmirrors. The 97.8% and 88.5% reflections result from, respectively, ascaling factor of 1 and 0.45 for the altered holes. The scaling factorcorresponds to a scaling of the hole diameter relative to a referencediameter for the array of holes. FIG. 9D presents a table ofreflectivity values for the example photonic crystal structure of FIG.9A that result from various scaling factors. The table shows that abroad range of reflectivity can be achieved using the approach of FIGS.9A-9C. However, other methods may be used to control the reflectivityproximate the end of the elongated slot. For example, the hole structureitself may be changed, such as by changing the periodicity of the arrayof holes.

The photonic crystal masers may also serve as part of a system forgenerating radio frequency (RF) electromagnetic radiation, especially ifa directed source of such radiation is desired. In some implementations,a system for generating radio frequency (RF) electromagnetic radiationincludes a maser having a photonic crystal structure and a vaportherein. More specifically, the photonic crystal structure is formed ofdielectric material and includes an array of cavities having a defectregion disposed therein and an elongated slot disposed in the defectregion. The array of cavities and the elongated slot define a waveguidehaving a waveguide mode. The vapor disposed in the elongated slotincludes one or more input electronic transitions and an outputelectronic transition coupled to the one or more input electronictransitions. The output electronic transition is operable to emit atarget RF electromagnetic radiation. Moreover, the output electronictransition is resonant with the waveguide mode of the waveguide. Themaser may be analogous to the example photonic crystal masers describedin relation to FIGS. 1A-9.

The system also includes a laser system configured to provide inputoptical signals to the elongated slot of the photonic crystal structure.The input optical signals are capable of exciting the one or more inputelectronic transitions of the vapor. The laser system may include afiber optic assembly that optically couples the laser system to theelongated slot. The system additionally includes signal processingelectronics in communication with the laser system and configured tocontrol one or more properties of the input optical signals. The one ormore properties may include at least one of an intensity, a phase, or afrequency. In some variations, the system includes a data interface incommunication with the signal processing electronics and configured toreceive signals representing the one or more properties of the inputoptical signals.

Now referring to FIG. 10, a schematic diagram is presented of an exampletesting system that includes a photonic crystal maser. The photoniccrystal maser may be disposed, entirely or in part, in an anechoicchamber that encloses a device-under-test (DUT). The photonic crystalmaser may be oriented to transmit an output beam (or RF pulses) to theDUT. The testing system includes a laser system having one or more pumplasers optically coupled to the photonic crystal maser, such as by fiberoptics. The laser system may also include one or more lasers opticallycoupled to predetermined locations in the anechoic chamber. The testingsystem includes signal processing electronics in communication with thelaser system and an interface (or a data interface) in communicationwith the signal processing electronics. In some variations, theinterface may also be in communication with the laser system.

Now referring to FIG. 11, a schematic diagram is presented of an exampletransceiver system that includes two transceivers, each having aphotonic crystal maser and a photonic crystal receiver. The transceiversmay be oriented towards each other, such as to allow the transmission ofRF signals therebetween. The photonic crystal maser may be analogous tothe example photonic crystal masers described in relation to FIGS. 1A-9,and the photonic crystal receiver may be analogous to the photoniccrystal receivers described in U.S. Pat. No. 11,137,432. Thetransceivers are optically coupled to a laser system, such as by fiberoptics. The laser system may include one or more pump lasers opticallycoupled to each photonic crystal maser. The laser system may alsoinclude one or more probe lasers and one or more coupling lasersoptically coupled to each photonic crystal receiver. The transceiversystem includes signal processing electronics in communication with thelaser system and an interface (or a data interface) in communicationwith the signal processing electronics. In some variations, theinterface may also be in communication with the laser system.

Now referring to FIG. 12, a schematic diagram is presented of a systemthat includes a photonic crystal maser and a vapor cell sensor. Thephotonic crystal maser may be oriented to transmit an output beam oftarget RF electromagnetic radiation (or RF pulses) to the vapor cellsensor. The system may include a laser system having one or more pumplasers optically coupled to the photonic crystal maser, such as by fiberoptics. The laser system may also include one or more probe lasers andone or more coupling lasers optically coupled to the vapor cell sensor,such as by fiber optics. The system includes signal processingelectronics in communication with the laser system and an interface (ora data interface) in communication with the signal processingelectronics. In some variations, the interface may also be incommunication with the laser system.

In some aspects of what is described, a photonic crystal maser may bedescribed by the following examples:

-   Example 1. A photonic crystal maser comprising:    -   a dielectric body comprising:        -   an array of cavities ordered periodically to define a            photonic crystal structure in the dielectric body,        -   a region in the array of cavities defining a defect in the            photonic crystal structure, and        -   an elongated slot through the region extending from a slot            opening in a surface of the dielectric body at least            partially through the dielectric body,        -   wherein the array of cavities and the elongated slot define            a waveguide having a waveguide mode;    -   an optical window covering the elongated slot and having a        window surface bonded to the surface of the dielectric body to        form a seal about the slot opening;    -   a vapor or a source of the vapor in the elongated slot, the        vapor comprising:        -   one or more input electronic transitions; and        -   an output electronic transition coupled to the one or more            input electronic transitions and operable to emit a target            radiofrequency (RF) electromagnetic radiation, the output            electronic transition resonant with the waveguide mode of            the waveguide; and    -   a laser configured to generate an optical signal capable of        exciting the one or more input electronic transitions of the        vapor.-   Example 2. The photonic crystal maser of example 1, wherein the    photonic crystal structure is configured to concentrate the target    RF electromagnetic radiation in the elongated slot.-   Example 3. The photonic crystal maser of example 1 or example 2,    -   wherein the region in the array of cavities extends along an        axis and the elongated slot is aligned parallel to the axis; and    -   wherein the photonic crystal structure is configured to decrease        a group velocity of the target RF electromagnetic along a        direction parallel to the axis.-   Example 4. The photonic crystal maser of example 1 or any one of    examples 2-3, wherein the cavities of the array are disposed on    respective sites of a two-dimensional lattice and the region is    defined by an absence of cavities on two or more contiguous sites of    the two-dimensional lattice.-   Example 5. The photonic crystal maser of example 1 or any one of    examples 2-4, wherein the array of cavities comprises one or more    offset cavities that are spatially offset from an ideal periodic    position in the array.-   Example 6. The photonic crystal maser of example 5, wherein the one    or more offset cavities reside nearest an end of the elongated slot    and have respective spatial offsets away from the end of the    elongated slot.-   Example 7. The photonic crystal maser of example 5, wherein the one    or more offset cavities reside nearest a side of the elongated slot    and have respective spatial offsets away from the side of the    elongated slot.-   Example 8. The photonic crystal maser of example 1 or any one of    examples 2-7, comprising an optical mirror disposed at an end of the    elongated slot.-   Example 9. The photonic crystal maser of example 8, wherein the    optical mirror is angled relative to an optical pathway defined by    the elongated slot.-   Example 10. The photonic crystal maser of example 8, wherein the    optical mirror is perpendicular to an optical pathway defined by the    elongated slot.-   Example 11. The photonic crystal maser of example 1 or any one of    examples 2-10, wherein the region in the array of cavities extends    along an axis and the elongated slot is aligned parallel to the    axis; and    -   wherein the dielectric body comprises an impedance-matching        structure that extends from an end of the dielectric body and is        aligned with the axis, the impedance-matching structure        configured to impedance match the target RF electromagnetic        radiation to an ambient environment of the photonic crystal        maser.-   Example 12. The photonic crystal maser of example 11, wherein the    impedance-matching structure terminates in a tapered end and    comprises:    -   a narrow portion aligned with the tapered end; and    -   an array of co-planar segments extending outward from the narrow        portion and having a periodic spacing therealong, the array of        co-planar segments configured to filter a polarization of the        target RF electromagnetic radiation.-   Example 13. The photonic crystal maser of example 1 or any one of    examples 2-12,    -   wherein the window surface is a first window surface;    -   wherein the optical window comprises a second window surface        opposite the first window surface; and    -   wherein the photonic crystal maser comprises a dielectric plate        separated from the second window surface by a gap.-   Example 14. The photonic crystal maser of example 1 or any one of    examples 2-13,    -   wherein the photonic crystal structure defines a photonic band        gap associated with a transverse magnetic (TM) mode of the        target RF electromagnetic radiation in the waveguide.-   Example 15. The photonic crystal maser of example 1 or any one of    examples 2-14,    -   wherein the photonic crystal structure defines a photonic band        gap associated with a transverse electric (TE) mode of the        target RF electromagnetic radiation in the waveguide.-   Example 16. The photonic crystal maser of example 1 or any one of    examples 2-15,    -   wherein the region forms a loop in the array of cavities and the        elongated slot extends along a loop axis of the loop to form a        looped slot; and    -   wherein the vapor or the source of the vapor is disposed in at        least a portion of the looped slot.-   Example 17. The photonic crystal maser of example 16,    -   wherein the looped slot is associated with first and second loop        directions along the loop axis, the first loop direction        opposite the second loop direction;    -   wherein the looped slot comprises first and second RF ports; and    -   wherein the photonic crystal maser comprises:        -   first and second directional couplers coupled to,            respectively, the first and second RF ports, the first            directional coupler configured to receive a first portion of            the target RF electromagnetic radiation traveling along the            first loop direction, the second directional coupler            configured to receive a second portion of the target RF            electromagnetic radiation traveling along the second loop            direction.-   Example 18. The photonic crystal maser of example 1 or any one of    examples 2-17,    -   wherein the surface of the dielectric body defines a cavity        opening for each of the array of cavities;    -   wherein the optical window covers each of the cavity openings;        and    -   wherein the window surface forms a seal about each of the cavity        openings.-   Example 19. The photonic crystal maser of example 1 or any one of    examples 2-17,    -   wherein the surface of the dielectric body is a first surface        and the dielectric body comprises a second surface opposite the        first surface;    -   wherein the elongated slot extends through the dielectric body        from the first surface to the second surface;    -   wherein the slot opening is a first slot opening and the second        surface of the dielectric body defines a second slot opening of        the elongated slot;    -   wherein the optical window is a first optical window and the        window surface is a first window surface; and    -   wherein the photonic crystal maser comprises a second optical        window covering the second slot opening and having a second        window surface bonded to the second surface to form a seal about        the second slot opening.-   Example 20. The photonic crystal maser of example 19,    -   wherein the first and second surfaces of the dielectric body        define, respectively, first and second cavity openings for each        of the array of cavities;    -   wherein the first and second optical windows cover,        respectively, each of the first and second cavity openings; and    -   wherein the first and second window surfaces form respective        seals about each of the first and second cavity openings.-   Example 21. The photonic crystal maser of example 1 or any one of    examples 2-20,    -   wherein the target RF electromagnetic radiation has a frequency        in a range from 100 MHz to 1 THz.-   Example 22. The photonic crystal maser of example 1 or any one of    examples 2-21,    -   wherein the vapor comprises a gas of alkali-metal atoms.

In some aspects of what is described, a method may be described by thefollowing examples:

-   Example 1. A method comprising:    -   receiving an optical signal into an elongated slot of a        dielectric body, the dielectric body comprising:        -   an array of cavities ordered periodically to define a            photonic crystal structure in the dielectric body,        -   a region in the array of cavities defining a defect in the            photonic crystal structure, and        -   the elongated slot, positioned in the region and extending            from a slot opening in a surface of the dielectric body at            least partially through the dielectric body,        -   wherein:            -   an optical window covers the elongated slot and has a                window surface bonded to a surface of the dielectric                body to form a seal about the slot opening, and            -   the array of cavities and the elongated slot define a                waveguide having a waveguide mode; and    -   emitting a target radio frequency (RF) electromagnetic radiation        from a vapor sealed in the elongated slot, the vapor comprising:        -   one or more input electronic transitions excited by the            optical signal, and        -   an output electronic transition coupled to the one or more            input electronic transitions and operable to emit the target            RF electromagnetic radiation, the output electronic            transition resonant with the waveguide mode of the            waveguide; and    -   amplifying the target RF electromagnetic radiation by resonating        at least a portion of the target RF electromagnetic radiation        between the output electronic transition and the waveguide mode.-   Example 2. The method of example 1, wherein receiving the optical    signal into the elongated slot comprises interacting the optical    signal with the vapor in the elongated slot.-   Example 3. The method of example 2, wherein interacting the optical    signal comprises propagating the optical signal along an optical    pathway defined by the elongated slot.-   Example 4. The method of example 1 or any one of examples 2-3,    wherein receiving the optical signal into the elongated slot    comprises reflecting the optical signal off a mirror disposed at an    end of the elongated slot.-   Example 5. The method of example 1 or any one of examples 2-4,    comprising:    -   directing, by operation of the waveguide, the target RF        electromagnetic radiation toward an end of the dielectric body.-   Example 6. The method of example 5,    -   wherein the region in the array of cavities extends along an        axis and the elongated slot is aligned parallel to the axis;    -   wherein the dielectric body comprises an impedance-matching        structure extending from the end of the dielectric body and        aligned with the axis; and    -   wherein the method comprises:        -   coupling the target RF electromagnetic radiation after            emission or amplification to the impedance-matching            structure; and        -   by operation of the impedance-matching structure, impedance            matching the coupled target RF electromagnetic radiation to            an ambient environment of the dielectric body.-   Example 7. The method of example 6, comprising:    -   filtering a polarization of the coupled target RF        electromagnetic radiation using a polarizer that is an integral        part of the impedance-matching structure.-   Example 8. The method of example 1 or any one of examples 2-7,    wherein amplifying the target RF electromagnetic radiation comprises    concentrating the target RF electromagnetic radiation in the    elongated slot.-   Example 9. The method of example 1 or any one of examples 2-8,    -   wherein the region in the array of cavities extends along an        axis and the elongated slot is aligned parallel to the axis; and    -   wherein amplifying the target RF electromagnetic radiation        comprises decreasing a group velocity of the target RF        electromagnetic radiation along a direction parallel to the        axis.-   Example 10. The method of example 1 or any one of examples 2-9,    -   wherein the array of cavities comprises one or more offset        cavities that are spatially offset from an ideal periodic        position in the array; and    -   wherein amplifying the target RF electromagnetic radiation        comprises reflecting the target RF electromagnetic radiation off        the offset cavities.-   Example 11. The method of example 1 or any one of examples 2-10,    -   wherein the region forms a loop in the array of cavities and the        elongated slot extends along a loop axis of the loop to form a        looped slot;    -   wherein the vapor is disposed in at least a portion of the        looped slot;    -   wherein the looped slot is associated with first and second loop        directions along the loop axis, the first loop direction        opposite the second loop direction; and    -   wherein the method comprises:        -   propagating a first portion of the target RF electromagnetic            radiation along the first loop direction, and        -   propagating a second portion of the target RF            electromagnetic radiation along the second loop direction.-   Example 12. The method of example 1 or any one of examples 2-11,    wherein the target RF electromagnetic radiation has a frequency in a    range from 100 MHz to 1 THz.-   Example 13. The method of example 1 or any one of examples 2-12,    wherein the vapor comprises a gas of alkali-metal atoms.

In some aspects of what is described, a system for generating radiofrequency electromagnetic radiation may be described by the followingexamples:

-   Example 1. A system for generating radio frequency (RF)    electromagnetic radiation, the system comprising:    -   a maser comprising:        -   a photonic crystal structure formed of dielectric material            and comprising:            -   an array of cavities having a defect region disposed                therein, and            -   an elongated slot disposed in the defect region,            -   wherein the array of cavities and the elongated slot                define a waveguide having a waveguide mode, and        -   a vapor disposed in the elongated slot and comprising:            -   one or more input electronic transitions, and            -   an output electronic transition coupled to the one or                more input electronic transitions and operable to emit a                target RF electromagnetic radiation, the output                electronic transition resonant with the waveguide mode                of the waveguide;    -   a laser system configured to provide input optical signals to        the elongated slot of the photonic crystal structure, the input        optical signals capable of exciting the one or more input        electronic transitions of the vapor;    -   signal processing electronics in communication with the laser        system and configured to control one or more properties of the        input optical signals, the one or more properties comprising at        least one of an intensity, a phase, or a frequency.-   Example 2. The system of example 1, comprising a data interface in    communication with the signal processing electronics and configured    to receive signals representing the one or more properties of the    input optical signals.-   Example 3. The system of example 1 or example 2, wherein the laser    system comprises a fiber optic assembly that optically couples the    laser system to the elongated slot.-   Example 4. The system of example 1 or any one of examples 2-3,    wherein the photonic crystal structure is configured to concentrate    the target RF electromagnetic radiation in the elongated slot.-   Example 5. The system of example 1 or any one of examples 2-4,    -   wherein the defect region in the array of cavities extends along        an axis and the elongated slot is aligned parallel to the axis;        and    -   wherein the photonic crystal structure is configured to decrease        a group velocity of the target RF electromagnetic radiation        along a direction parallel to the axis.-   Example 6. The system of example 1 or any one of examples 2-5,    wherein the cavities of the array are disposed on respective sites    of a two-dimensional lattice and the defect region is defined by an    absence of cavities on two or more contiguous sites of the    two-dimensional lattice.-   Example 7. The system of example 1 or any one of examples 2-6,    wherein the array of cavities comprises one or more offset cavities    that are spatially offset from an ideal periodic position in the    array.-   Example 8. The system of example 7, wherein the one or more offset    cavities reside nearest an end of the elongated slot and have    respective spatial offsets away from the end of the elongated slot.-   Example 9. The system of example 7, wherein the one or more offset    cavities reside nearest a side of the elongated slot and have    respective spatial offsets away from the side of the elongated slot.-   Example 10. The system of example 1 or any one of examples 2-9,    wherein the photonic crystal structure comprises an optical mirror    disposed at an end of the elongated slot.-   Example 11. The system of example 1 or any one of examples 2-10,    -   wherein the defect region in the array of cavities extends along        an axis and the elongated slot is aligned parallel to the axis;        and    -   wherein the maser comprises an impedance-matching structure that        extends from an end of the maser and is aligned with the        elongated slot, the impedance-matching structure configured to        impedance match the target RF electromagnetic radiation to an        ambient environment of the maser.-   Example 12. The system of example 11, wherein the impedance-matching    structure terminates in a tapered end and comprises:    -   a narrow portion aligned with the tapered end; and    -   an array of co-planar segments extending outward from the narrow        portion and having a periodic spacing therealong, the array of        co-planar segments configured to filter a polarization of the        target RF electromagnetic radiation.-   Example 13. The system of example 1 or any one of examples 2-12,    -   wherein the defect region forms a loop in the array of cavities        and the elongated slot extends along a loop axis of the loop to        form a looped slot; and    -   wherein the vapor is disposed in at least a portion of the        looped slot.-   Example 14. The system of example 13,    -   wherein the looped slot is associated with first and second loop        directions along the loop axis, the first loop direction        opposite the second loop direction;    -   wherein the looped slot comprises first and second RF ports; and    -   wherein the maser comprises:        -   first and second directional couplers coupled to,            respectively, the first and second RF ports, the first            directional coupler configured to receive a first portion of            the target RF electromagnetic radiation traveling along the            first loop direction, the second directional coupler            configured to receive a second portion of the target RF            electromagnetic radiation traveling along the second loop            direction.-   Example 15. The system of example 1 or any one of examples 2-14,    wherein the target RF electromagnetic radiation has a frequency in a    range from 100 MHz to 1 THz.-   Example 16. The system of example 1 or any one of examples 2-15,    wherein the vapor comprises a gas of alkali-metal atoms.

In some aspects of what is described, a method may be described by thefollowing examples:

-   Example 1. A method comprising:    -   generating, by operation of a laser system, input optical        signals capable of exciting one or more input electronic        transitions of a vapor, the vapor part of a maser that        comprises:        -   a photonic crystal structure formed of dielectric material            and comprising:            -   an array of cavities having a defect region disposed                therein, and            -   an elongated slot disposed in the defect region,        -   wherein:            -   the array of cavities and the elongated slot define a                waveguide having a waveguide mode, and            -   the vapor is disposed in the elongated slot and                comprises:                -   the one or more input electronic transitions, and                -   an output electronic transition coupled to the one                    or more input electronic transitions and operable to                    emit a target radio frequency (RF) electromagnetic                    radiation, the output electronic transition resonant                    with the waveguide mode of the waveguide;    -   controlling, by operation of signal processing electronics, one        or more properties of the input optical signals, the signal        processing electronics in communication with the laser system,        the one or more properties comprising at least one of an        intensity, a phase, or a frequency; and    -   emitting, by operation of the output electronic transition, the        target RF electromagnetic radiation from the vapor in response        to receiving the input optical signals into the elongated slot.-   Example 2. The method of example 1, comprising:    -   receiving, at a data interface, signals representing the one or        more properties of the input optical signals, the data interface        in communication with the signal processing electronics.-   Example 3. The method of example 1 or example 2,    -   wherein the one or more properties of the input optical signals        comprise an intensity of the optical signals;    -   wherein controlling the one or more properties of the input        optical signals comprises modulating the intensity of the input        optical signals to produce pulses of input optical signals; and    -   wherein emitting the target RF electromagnetic radiation        comprises emitting pulses of the target RF electromagnetic        radiation in response to receiving the pulses of input optical        signals into the elongated slot.-   Example 4. The method of example 1 or any one of examples 2-3,    comprising:    -   amplifying the target RF electromagnetic radiation by resonating        at least a portion of the target RF electromagnetic radiation        between the output electronic transition and the waveguide mode.-   Example 5. The method of example 4, wherein amplifying the target RF    electromagnetic radiation comprises concentrating the target RF    electromagnetic radiation in the elongated slot.-   Example 6. The method of example 4 or example 5,    -   wherein the defect region in the array of cavities extends along        an axis and the elongated slot is aligned parallel to the axis;        and    -   wherein amplifying the target RF electromagnetic radiation        comprises decreasing a group velocity of the target RF        electromagnetic radiation along a direction parallel to the        axis.-   Example 7. The method of example 4 or any one of examples 5-6,    -   wherein the array of cavities comprises one or more offset        cavities that are spatially offset from an ideal periodic        position in the array; and    -   wherein amplifying the target RF electromagnetic radiation        comprises reflecting the target RF electromagnetic radiation off        the offset cavities.-   Example 8. The method of example 1 or any one of examples 2-7,    -   wherein the defect region forms a loop in the array of cavities        and the elongated slot extends along a loop axis of the loop to        form a looped slot;    -   wherein the vapor is disposed in at least a portion of the        looped slot;    -   wherein the looped slot is associated with first and second loop        directions along the loop axis, the first loop direction        opposite the second loop direction; and    -   wherein the method comprises:        -   propagating a first portion of the target RF electromagnetic            radiation along the first loop direction, and        -   propagating a second portion of the target RF            electromagnetic radiation along the second loop direction.-   Example 9. The method of example 1 or any one of examples 2-8,    comprising:    -   directing, by operation of the waveguide, the target RF        electromagnetic radiation toward an end of the maser.-   Example 10. The method of example 9,    -   wherein the region in the array of cavities extends along an        axis and the elongated slot is aligned parallel to the axis;    -   wherein the maser comprises an impedance-matching structure that        extends from the end of the maser and is aligned with the axis;        and    -   wherein the method comprises:        -   coupling the target RF electromagnetic radiation to the            impedance-matching structure; and        -   by operation of the impedance-matching structure, impedance            matching the coupled target RF electromagnetic radiation to            an ambient environment of the dielectric body.-   Example 11. The method of example 10, comprising:

filtering a polarization of the coupled target RF electromagneticradiation using a polarizer that is an integral part of theimpedance-matching structure.

-   Example 12. The method of example 1 or any one of examples 2-11,    comprises:

conveying, by operation of a fiber optic assembly, the input opticalsignals from the laser system to the elongated slot.

-   Example 13. The method example 1 or any one of examples 2-12,    wherein the target RF electromagnetic radiation has a frequency in a    range from 100 MHz to 1 THz.-   Example 14. The method of example 1 or any one of examples 2-13,    wherein the vapor comprises a gas of alkali-metal atoms.

While this specification contains many details, these should not beunderstood as limitations on the scope of what may be claimed, butrather as descriptions of features specific to particular examples.Certain features that are described in this specification or shown inthe drawings in the context of separate implementations can also becombined. Conversely, various features that are described or shown inthe context of a single implementation can also be implemented inmultiple embodiments separately or in any suitable sub-combination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the implementations described above should not beunderstood as requiring such separation in all implementations, and itshould be understood that the described program components and systemscan generally be integrated together in a single product or packagedinto multiple products.

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications can be made. Accordingly, otherembodiments are within the scope of the following claims.

What is claimed is:
 1. A photonic crystal maser comprising: a dielectricbody comprising: an array of cavities ordered periodically to define aphotonic crystal structure in the dielectric body, a region in the arrayof cavities defining a defect in the photonic crystal structure, and anelongated slot through the region extending from a slot opening in asurface of the dielectric body at least partially through the dielectricbody, wherein the array of cavities and the elongated slot define awaveguide having a waveguide mode; an optical window covering theelongated slot and having a window surface bonded to the surface of thedielectric body to form a seal about the slot opening; a vapor or asource of the vapor in the elongated slot, the vapor comprising: one ormore input electronic transitions; and an output electronic transitioncoupled to the one or more input electronic transitions and operable toemit a target radiofrequency (RF) electromagnetic radiation, the outputelectronic transition resonant with the waveguide mode of the waveguide;and a laser configured to generate an optical signal capable of excitingthe one or more input electronic transitions of the vapor.
 2. Thephotonic crystal maser of claim 1, wherein the cavities of the array aredisposed on respective sites of a two-dimensional lattice and the regionis defined by an absence of cavities on two or more contiguous sites ofthe two-dimensional lattice.
 3. The photonic crystal maser of claim 1,wherein the photonic crystal structure is configured to concentrate thetarget RF electromagnetic radiation in the elongated slot.
 4. Thephotonic crystal maser of claim 1, wherein the region in the array ofcavities extends along an axis and the elongated slot is alignedparallel to the axis; and wherein the photonic crystal structure isconfigured to decrease a group velocity of the target RF electromagneticalong a direction parallel to the axis.
 5. The photonic crystal maser ofclaim 1, wherein the array of cavities comprises one or more offsetcavities that are spatially offset from an ideal periodic position inthe array.
 6. The photonic crystal maser of claim 5, wherein the one ormore offset cavities reside nearest an end of the elongated slot andhave respective spatial offsets away from the end of the elongated slot.7. The photonic crystal maser of claim 5, wherein the one or more offsetcavities reside nearest a side of the elongated slot and have respectivespatial offsets away from the side of the elongated slot.
 8. Thephotonic crystal maser of claim 1, comprising an optical mirror disposedat an end of the elongated slot.
 9. The photonic crystal maser of claim8, wherein the optical mirror is angled relative to an optical pathwaydefined by the elongated slot.
 10. The photonic crystal maser of claim8, wherein the optical mirror is perpendicular to an optical pathwaydefined by the elongated slot.
 11. The photonic crystal maser of claim1, wherein the region in the array of cavities extends along an axis andthe elongated slot is aligned parallel to the axis; and wherein thedielectric body comprises an impedance-matching structure that extendsfrom an end of the dielectric body and is aligned with the axis, theimpedance-matching structure configured to impedance match the target RFelectromagnetic radiation to an ambient environment of the photoniccrystal maser.
 12. The photonic crystal maser of claim 11, wherein theimpedance-matching structure terminates in a tapered end and comprises:a narrow portion aligned with the tapered end; and an array of co-planarsegments extending outward from the narrow portion and having a periodicspacing therealong, the array of co-planar segments configured to filtera polarization of the target RF electromagnetic radiation.
 13. Thephotonic crystal maser of claim 1, wherein the window surface is a firstwindow surface; wherein the optical window comprises a second windowsurface opposite the first window surface; and wherein the photoniccrystal maser comprises a dielectric plate separated from the secondwindow surface by a gap.
 14. The photonic crystal maser of claim 1,wherein the photonic crystal structure defines a photonic band gapassociated with a transverse magnetic (TM) mode of the target RFelectromagnetic radiation in the waveguide.
 15. The photonic crystalmaser of claim 1, wherein the photonic crystal structure defines aphotonic band gap associated with a transverse electric (TE) mode of thetarget RF electromagnetic radiation in the waveguide.
 16. The photoniccrystal maser of claim 1, wherein the vapor comprises a gas ofalkali-metal atoms.
 17. The photonic crystal maser of claim 1, whereinthe region forms a loop in the array of cavities and the elongated slotextends along a loop axis of the loop to form a looped slot; and whereinthe vapor or the source of the vapor is disposed in at least a portionof the looped slot.
 18. The photonic crystal maser of claim 17, whereinthe looped slot is associated with first and second loop directionsalong the loop axis, the first loop direction opposite the second loopdirection; wherein the looped slot comprises first and second RF ports;and wherein the photonic crystal maser comprises: first and seconddirectional couplers coupled to, respectively, the first and second RFports, the first directional coupler configured to receive a firstportion of the target RF electromagnetic radiation traveling along thefirst loop direction, the second directional coupler configured toreceive a second portion of the target RF electromagnetic radiationtraveling along the second loop direction.
 19. The photonic crystalmaser of claim 1, wherein the surface of the dielectric body is a firstsurface and the dielectric body comprises a second surface opposite thefirst surface; wherein the elongated slot extends through the dielectricbody from the first surface to the second surface; wherein the slotopening is a first slot opening and the second surface of the dielectricbody defines a second slot opening of the elongated slot; wherein theoptical window is a first optical window and the window surface is afirst window surface; and wherein the photonic crystal maser comprises asecond optical window covering the second slot opening and having asecond window surface bonded to the second surface to form a seal aboutthe second slot opening.
 20. A method comprising: receiving an opticalsignal into an elongated slot of a dielectric body, the dielectric bodycomprising: an array of cavities ordered periodically to define aphotonic crystal structure in the dielectric body, a region in the arrayof cavities defining a defect in the photonic crystal structure, and theelongated slot, positioned in the region and extending from a slotopening in a surface of the dielectric body at least partially throughthe dielectric body, wherein: an optical window covers the elongatedslot and has a window surface bonded to a surface of the dielectric bodyto form a seal about the slot opening, and the array of cavities and theelongated slot define a waveguide having a waveguide mode; and emittinga target radio frequency (RF) electromagnetic radiation from a vaporsealed in the elongated slot, the vapor comprising: one or more inputelectronic transitions excited by the optical signal, and an outputelectronic transition coupled to the one or more input electronictransitions and operable to emit the target RF electromagneticradiation, the output electronic transition resonant with the waveguidemode of the waveguide; and amplifying the target RF electromagneticradiation by resonating at least a portion of the target RFelectromagnetic radiation between the output electronic transition andthe waveguide mode.
 21. The method of claim 20, wherein receiving theoptical signal into the elongated slot comprises interacting the opticalsignal with the vapor in the elongated slot.
 22. The method of claim 21,wherein interacting the optical signal comprises propagating the opticalsignal along an optical pathway defined by the elongated slot.
 23. Themethod of claim 20, wherein receiving the optical signal into theelongated slot comprises reflecting the optical signal off a mirrordisposed at an end of the elongated slot.
 24. The method of claim 20,comprising: directing, by operation of the waveguide, the target RFelectromagnetic radiation toward an end of the dielectric body.
 25. Themethod of claim 24, wherein the region in the array of cavities extendsalong an axis and the elongated slot is aligned parallel to the axis;wherein the dielectric body comprises an impedance-matching structureextending from the end of the dielectric body and aligned with the axis;and wherein the method comprises: coupling the target RF electromagneticradiation after emission or amplification to the impedance-matchingstructure; and by operation of the impedance-matching structure,impedance matching the coupled target RF electromagnetic radiation to anambient environment of the dielectric body.
 26. The method of claim 25,comprising: filtering a polarization of the coupled target RFelectromagnetic radiation using a polarizer that is an integral part ofthe impedance-matching structure.
 27. The method of claim 20, whereinamplifying the target RF electromagnetic radiation comprisesconcentrating the target RF electromagnetic radiation in the elongatedslot.
 28. The method of claim 20, wherein the region in the array ofcavities extends along an axis and the elongated slot is alignedparallel to the axis; and wherein amplifying the target RFelectromagnetic radiation comprises decreasing a group velocity of thetarget RF electromagnetic radiation along a direction parallel to theaxis.
 29. The method of claim 20, wherein the array of cavitiescomprises one or more offset cavities that are spatially offset from anideal periodic position in the array; and wherein amplifying the targetRF electromagnetic radiation comprises reflecting the target RFelectromagnetic radiation off the offset cavities.
 30. The method ofclaim 20, wherein the vapor comprises a gas of alkali-metal atoms.